navigation is the search results plus the referrer — one index for search and navigation
Theorem.navigation is the search results plus the referrer — one index for search and navigation.
Proof.navigation IS the search results plus the referrer (user, 2026-07-25: "navigation is based on the search results themselves and the referrer"). The outgoing edges of a node are the BM25-ranked search results for its query (you navigate by RELEVANCE, not a hand-built menu), and the incoming edge is the referrer; the (referrer, query) pair content-addresses the nav state (same pair → one receipt, different referrer → different). One private BM25 index drives both search and navigation, so there is no second topology to maintain; deterministic and client-side with no egress. SCOPE: navigation edges are lexical BM25 relevance plus the runtime referrer — NOT a curated menu, NOT a neural recommender — and the referrer collapses at navigation time. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/wind/site/index.ts#navigationFromSearchResultsAndReferrer
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"navigation is the search results plus the referrer — one index for search and navigation" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation navigationFromSearchResultsAndReferrer.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (navigationFromSearchResultsAndReferrer @ src/wind/site) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes navigationFromSearchResultsAndReferrer (src/wind/site/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.